In a large bowl, combine the water, yeast, sugar, and 1 tablespoon oil and stir to combine. Let sit until the mixture is foamy, about 5 minutes.
Add 1 1/2 cups of the flour and the salt, mixing by hand until it is all incorporated and the mixture is smooth. Continue adding the flour, 1/4 cup at a time, working the dough after each addition, until all the flour is incorporated but the dough is still slightly sticky. Turn the dough out onto a lightly floured surface and knead until smooth but still slightly tacky, 3 to 5 minutes.
Oil a large mixing bowl with the remaining 1 1/2 teaspoons olive oil. Place the dough in the bowl and turn to oil all sides. Cover the bowl with plastic wrap and set in a warm, draft-free place until nearly doubled in size, 1 to 1 1/2 hours.
To make the Stromboli:
Preheat the oven to 375 degrees F. Grease a large baking sheet and set aside.
In a large skillet, cook the sausage over medium-high heat until browned and the fat is rendered, about 5 minutes. Remove with a slotted spoon and drain well on paper towels. Discard all but 1 tablespoon of fat from the pan. Add the onions, bell peppers, and jalapenos and cook, stirring, until very soft, 4 to 5 minutes. Add the garlic and Italian seasoning and cook, stirring, for 1 minute. Remove from the heat and cool.
Punch down the dough and divide half. On a lightly floured surface, roll out half of the dough to a large rectangle, about 10 by 14 inches. Spread half of the cooled sausage mixture across the dough leaving a 1-inch border. Overlapping slightly, layer half of the ham, pepperoni, olives, provolone and mozzarella cheeses over the top. Using a pastry brush, paint the border of 1 long edge with egg wash. Starting at the opposite long end without egg wash, roll up the dough into a cylinder, pinching the edges to seal. Place on the prepared baking sheet and repeat with the remaining ingredients. Let the dough rise, 20 to 30 minutes.
Brush the top of each stromboli with egg wash. Bake until nearly completely golden brown and starting to crisp, about 20 minutes. Sprinkle each stromboli with Parmesan cheese and return to the oven until the cheese is melted and the dough is golden brown, about 5 minutes.
Remove from the oven and let stand 10 minutes. Slice thickly and serve.